2
Eric Xing
© Eric Xing @ CMU, 2006-2008
3
z
Directed edges
give
causality
relationships (
Bayesian
Network
or
Directed Graphical Model
):
z
Undirected edges
simply give
correlations
between variables
(
Markov Random Field
or
Undirected Graphical model
):
Two types of GMs
X1
X2
X3
X4
X5
X6
X7
X8
Receptor A
Kinase C
TF F
Gene G
Gene H
Kinase E
Kinase D
Receptor B
X1
X2
X3
X4
X5
X6
X7
X8
Receptor A
Kinase C
TF F
Gene G
Gene H
Kinase E
Kinase D
Receptor B
P
(
X
1
, X
2
, X
3
, X
4
, X
5
, X
6
, X
7
, X
8
)
= P
(
X
1
)
P
(
X
2
)
P
(
X
3
| X
1
)
P
(
X
4
| X
2
)
P
(
X
5
| X
2
)
P
(
X
6
| X
3
, X
4
)
P
(
X
7
| X
6
)
P
(
X
8
| X
5
, X
6
)
P
(
X
1
, X
2
, X
3
, X
4
, X
5
, X
6
, X
7
, X
8
)
=
1/Z
exp{
E
(
X
1
)
+E
(
X
2
)
+E
(
X
3
, X
1
)+
E
(
X
4
, X
2
)
+E
(
X
5
, X
2
)
+
E
(
X
6
, X
3
, X
4
)+
E
(
X
7
, X
6
)+
E
(
X
8
, X
5
, X
6
)}
Eric Xing
© Eric Xing @ CMU, 2006-2008
4
Structure:
DAG
• Meaning: a node is
conditionally independent
of every other node in the
network outside its
Markov
blanket
• Local conditional distributions
(
CPD
) and the
DAG
completely determine the
joint
dist.
•G
i
ve
causality
relationships,
and facilitate a
generative
process
X
Y
1
2
Descendent
Ancestor
Parent
Children's co-parent
Child
Bayesian Network:
Conditional
Independence Semantics